On the Properties of Special Functions on the linear-type lattices

Abstract

We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to $q$-classical polynomials are given.

References in corpus (1)

• Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra

Cited by in corpus (1)

• Recurrence Relations of the Hypergeometric-type functions on the quadratic-type lattices